DIMENSION PRINTS OF FRACTAL SETS

Dimension prints were developed in 1988 to distinguish between differe nt fractal sets in Euclidean spaces having the same Hausdorff dimensio n but with very different geometric characteristics. In this paper we compute the dimension prints of some fractal sets, including generaliz ed Cantor sets on the unit circle S1 in R2 and the graphs of generaliz ed Lebesgue functions, also in R2. In this second case we show that th e dimension print for the graphs of the Lebesgue functions can approac h the maximal dimension print of a set of dimension 1. We study the di mension prints of Cartesian products of linear Borel sets and obtain t he exact dimension print when each linear set has positive measure in its dimension and the dimension of the Cartesian product is the sum of the dimensions of the factors.